- #1
Stephanus
- 1,316
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Dear PF Forum,
I'd like to know how to measure speed only by doppler effect.
What if we don't know the distance?
If we look this diagram on our computer screen, we'll know everything. Distance, speed, time dilation event relative simultaneity of event. But here, there are no relative simultaneity of events, because they are all time like.
Here, Green (G) will send a signal to Blue (B) everytime G receives B signal.
And B can't rely on the frequency of G signal, it might, it might not be same. For example B signal is at 100 MHz, and G send its own signal regardless what B sends, say 50MHz.
And this is all that B can see:
B sends its clock time then, G sends back B's clock time.
B can work out the speed by this formula
##f = \frac{1+V}{1-V}; 4 = \frac{1+V}{1-V}; V=\frac{3}{5}##
Time A column is B's clock when Blue receives the signal.
Read B column is the clock when Blue sent the signal.
Ok, it makes sense. Once the light cone from G entering B world line, the frequency changes to 4, forever.
Here at E2, actually Blue doesn't have to wait until E3, to know that the frequency changes. Blue could have sends signal at 1 pico seconds interval instead of 200 seconds interval. So right after E2, Blue can already detect the changing frequencey.
But I see something strange with this diagram.
Here is what B reads from the signal from G
The instant Blue moves the frequency changes to 2.
After sometime the signal from the time when B moves is received by B, the frequency changes to 4.
So, there are times between (E2 and E4) when Blue miscalculates the speed if using the same method as above picture.
E4 is the event when B receives the bounce back signal from when B started to move.
When F = 2, V is 1/3
When F = 4, V is 3/5
Where did I go wrong?
Thanks.
I'd like to know how to measure speed only by doppler effect.
What if we don't know the frequency?Nugatory said:
What if we don't know the distance?
If we look this diagram on our computer screen, we'll know everything. Distance, speed, time dilation event relative simultaneity of event. But here, there are no relative simultaneity of events, because they are all time like.
Here, Green (G) will send a signal to Blue (B) everytime G receives B signal.
And B can't rely on the frequency of G signal, it might, it might not be same. For example B signal is at 100 MHz, and G send its own signal regardless what B sends, say 50MHz.
And this is all that B can see:
B sends its clock time then, G sends back B's clock time.
Code:
Events Time A Diff Freq Read B
E1 700 .. 1 -1100
E2 900 200 1 > 4 -900
E3 950 50 4 -700
E4 1125 … 0
E5 1175 50 4 200##f = \frac{1+V}{1-V}; 4 = \frac{1+V}{1-V}; V=\frac{3}{5}##
Time A column is B's clock when Blue receives the signal.
Read B column is the clock when Blue sent the signal.
Ok, it makes sense. Once the light cone from G entering B world line, the frequency changes to 4, forever.
Here at E2, actually Blue doesn't have to wait until E3, to know that the frequency changes. Blue could have sends signal at 1 pico seconds interval instead of 200 seconds interval. So right after E2, Blue can already detect the changing frequencey.
But I see something strange with this diagram.
Here is what B reads from the signal from G
Code:
Events Time A Diff Freq Read B
E1 -200 … 1 -2000
E2 0 200 1 -> 2 -1800
E3 100 100 2 -1600
E4 900 … 0
E5 950 50 4 200After sometime the signal from the time when B moves is received by B, the frequency changes to 4.
So, there are times between (E2 and E4) when Blue miscalculates the speed if using the same method as above picture.
E4 is the event when B receives the bounce back signal from when B started to move.
When F = 2, V is 1/3
When F = 4, V is 3/5
Where did I go wrong?
Thanks.
Last edited:
